Signal processing generally encompasses collecting, organizing, transforming and summarizing raw input data to produce meaningful or useful information, or output data. Signal processing is the enabling technology for the generation, transformation, and interpretation of information. Signal processing typically uses computational or heuristic representations and techniques to acquire, extract, represent, model or analyze data embedded in an analog or digital signals, including, for example, audio, image, video, controls, radio frequency, and other electrical signals.
In general, signal processing entails processes such as sampling sensor and instrument signals; analog-to-digital (A/D or ADC) and digital-to-analog (D/A or DAC) conversion of signals; filtering signals for the purpose of noise reduction, enhancement, reconstruction of the original signal or an approximation of the signal, and the like. Computational techniques and mathematical models employed include, for example, arithmetic operations, differential and integral calculus, differential equations, transform theory, time-frequency analysis of non-stationary signals, spectral analysis, probability and statistical analysis, vector analysis and linear algebra, parametric signal modeling, detection theory, estimation theory, optimization, and other numerical methods.
Digital signal processing (DSP) typically is carried out by general purpose computers or specialized controllers. DSP makes use of discrete mathematics, including the representation of discrete time series, discrete frequency, and other discrete domain signals as a sequence of numbers or symbols and the processing of these signals. Discrete-time signal processing generally applies to sampled signals, such as signals generated by electrical, optical, or electromechanical sensors.
Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems in the time, frequency, or spatio-temporal domains. Nonlinear systems produce relatively complex signal characteristics that in some cases cannot be modeled or analyzed using linear methods.
The Hilbert transform is a linear operator that shifts the phase of frequency components of a function or signal in the same domain as the original function or signal. Complex, sequential, discrete pairs, [u(t), û(t)] or [u(t), Hu(t)], in which the real part is represented by the original function or signal and the imaginary part is represented by the discrete Hilbert transform of the function or signal compose an analytical signal. The Hilbert transformed series has the same amplitude and frequency content as the original function or signal, and includes phase information that correlates to the phase of the original function or signal.
In general, the Hilbert transform is useful in calculating instantaneous attributes of a time series, in particular, amplitude and frequency. The amplitude of the analytical signal is equal to the instantaneous amplitude of the original signal, and the time rate of change of the phase angle of the analytical signal is equal to the instantaneous frequency of the original signal.
Cardiovascular periodicity generally refers to the nearly regular, recurrent blood pressure and volume pulses induced by the heart. The time length of each period between consecutive individual heart beats is commonly referred to as the interbeat interval (IBI, or RR interval). The heart rate is the inverse of the cardiovascular periodicity.
During normal heart functioning, there is some variation in the continuous time series of IBI values. This natural variation is known as heart rate variability (HRV). Relatively noisy or low-amplitude sensor signals can add measurement error that further detracts from the nearly periodic nature of the observed heart beat signal. Thus, the observed heart beat sensor signal typically represents a quasiperiodic function. That is, the signal is similar to a periodic function, but displays irregular periodicity and does not meet the strict definition of a periodic function that recurs at regular intervals. Quasiperiodic behavior includes a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurement.
The time intervals between consecutive heart beats are customarily measured in an electrocardiogram (ECG or EKG) from the initiation of each of two consecutive QRS complexes, corresponding to the contraction of the heart ventricles, each of which typically includes three component waveforms (the Q-wave, R-wave and S-wave). However, the initiation of the QRS complex can be difficult to locate in relatively noisy or low-amplitude sensor signals, which can lead to measurement error. Thus, IBI sometimes is measured between R-wave peaks in consecutive heart beats to reduce measurement error.
IBI can also be determined from a peripheral pulse measurement, such as a digital volume pulse measurement, such as a photoplethysmogram (PPG), an optically obtained plethysmogram, or volumetric measurement of an organ. The pulse oximeter, a known type of PPG sensor, illuminates the skin with one or more colors of light and measures changes in light absorption at each wavelength. The PPG sensor illuminates the skin, for example, using an optical emitter, such as a light-emitting diode (LED), and measures either the amount of light transmitted through a relatively thin body segment, such as a finger or earlobe, or the amount of light reflected from the skin, for example, using a photodetector, such as a photodiode. PPG sensors have been used to monitor respiration and heart rates, blood oxygen saturation, hypovolemia, and other circulatory conditions.
Conventional PPGs typically monitor the perfusion of blood to the dermis and subcutaneous tissue of the skin, which can be used to detect, for example, the change in volume corresponding to the pressure pulses of consecutive cardiac cycles of the heart. If the PPG is attached without compressing the skin, a secondary pressure peak can also be seen from the venous plexus. A microcontroller typically processes and calculates the primary peaks in the waveform signal to count heart beats per minute (bpm).
Offsets, or DC shifts, can occur in biophysiological sensor signals as a result of inconsistencies in the interface between a subject and a sensor, such as an ECG electrode or a PPG optical sensor. The subject may include, but not limited to, a person, an animal, and a living organism. As a result, sensor designs typically must ensure a reliable mechanical interface between the subject and the sensor. In the case of some wearable devices with biophysiological sensors, including, for example, wrist-based wearables, there is a direct relationship between comfort (corresponding to a relatively loose attachment) and a reliable mechanical interface (corresponding to a relatively tight attachment).